電大歷年試題——經(jīng)濟(jì)數(shù)學(xué)基礎(chǔ) 線性代數(shù)小抄

1、電大歷年試題經(jīng)濟(jì)數(shù)學(xué)基礎(chǔ) 線性代數(shù)一、 單項(xiàng)選擇題：1、設(shè)a是mn矩陣，b是st矩陣,且有意義，則c是（ ）矩陣. a. mt b. tm c. ns d. sn2、設(shè)a是可逆矩陣，且a+ab=i,則=( ). a.b b.1+b c.i+b d.3、設(shè)a= ，則r(a)=( ). a.0 b.1 c.2 d.34、以下結(jié)論或等式正確的是（ ）. a.若a,b均為零矩陣，則有a=b b.若ab=ac,且ao，則b=cc.對(duì)角矩陣是對(duì)稱矩陣 d.若ao，bo,則abo 5、設(shè)a,b均為n階可逆矩陣，則下列等式成立的是（ ）. a. b. c. d.ab=ba 6、設(shè)a為32矩陣，b為23矩陣，則

2、下列運(yùn)算中（ ）可以進(jìn)行. a.ab b.a+b c. d. 7、設(shè)a,b為同階可逆矩陣，則下列等式成立的是（ ）. a. b.c. d. ( c. ) 8、設(shè)a為34矩陣，b為52矩陣，且乘積矩陣有意義，則c為（ ）矩陣. a.42 b.24 c.35 d.53 9、設(shè)a為34矩陣，b為52矩陣，且乘積矩陣有意義，則c為（ ）矩陣. a.45 b.53 c.54 d.42 10、設(shè)a,b為同階方陣，則下列命題正確的是（ ）. a.若ab=o,則必有a=o或b=o b.若abo,則必有ao,且boc.若秩（a）o,秩(b)o,則秩(ab)o d. 11、用消元法解方程組，得到解為（ ）. a.

3、 b. c. d. 12、設(shè)線性方程組ax=b的增廣矩陣為 ，則此線性方程組的一般解中自由未知量的個(gè)數(shù)為（ ）. a.1 b.2 c.3 d.4 13、線性方程組 =的解的情況是（ ）. a.無(wú)解 b.有無(wú)窮多解 c.只有0解 d.有唯一解 14、線性方程組解的情況是（ ）. a. 有無(wú)窮多解 b. 只有零解 c. 有唯一解 d. 無(wú)解 15、設(shè)線性方程組ax=b有唯一解，則相應(yīng)的齊次方程組ax=o（ ）. a.無(wú)解 b. 有非零解 c. 只有零解 d.解不能確定 16、若線性方程組的增廣矩陣為 （或 ）,則當(dāng)=（ ）時(shí)線性方程組無(wú)解. a. b.0 c.1 d.2 17、若線性方程組的增廣矩

4、陣為 ，則當(dāng)=（ ）時(shí)線性方程組無(wú)解. a.3 b.-3 c.1 d.-1 18、若線性方程組的增廣矩陣為 ，則當(dāng)=（ ）時(shí)線性方程組有無(wú)窮多解. a.1 b.4 c.2 d. 19、線性方程組解的情況是（ ）. a.無(wú)解 b. 只有0解 c. 有唯一解 d. 有無(wú)窮多解20、設(shè)a= ，則r(a)=( ). a.0 b.1 c.2 d.321、設(shè)a= ，則r(a)=( ). a.1 b.2 c.3 d.4 二、填空題： 1、矩陣 的秩為 . 2、設(shè)a= ，當(dāng)= 時(shí)，a是對(duì)稱矩陣. 3、設(shè)a= ，當(dāng)= 時(shí)，a是對(duì)稱矩陣. 4、兩個(gè)矩陣a、b既可相加又可相乘的充分必要條件是 . 5、設(shè)矩陣a= ，

5、i為單位矩陣，則 . 6、設(shè)a,b均為n階矩陣，則等式成立的充分必要條件是 . 7、設(shè)矩陣a可逆，b是a的逆矩陣，則= . 8、設(shè)a= ，則r(a)= . 9、已知齊次線性方程組ax=o中a為35矩陣，且該方程組有非0解，則r(a) . 10、n元齊次線性方程組ax=o有非零解的充分必要條件是r(a) . 11、線性方程組ax=b有解的充分必要條件是 . 12、齊次線性方程組ax=o（a是mn）只有零解的充分必要條件是 . 13、齊次線性方程組ax=o的系數(shù)矩陣為a= ，則此方程組的一般解為 .( 或則此方程組的一般解中自由未知量的個(gè)數(shù)為 .) 14、設(shè)齊次線性方程組,且r(a)=rn，則其一

6、般解中的自由未知量的個(gè)數(shù)等于 . 15、若線性方程組有非零解，則= . 16、若n元線性方程組ax=o滿足r(a) n，則該線性方程組 . 17、設(shè)齊次線性方程組，且r(a)=2，則方程組一般解中的自由未知量的個(gè)數(shù)為 . 18、線性方程組ax=b的增廣矩陣化成階梯形矩陣后為 則當(dāng)d = 時(shí)，方程組ax=b有無(wú)窮多解. 19.若a為n階可逆矩陣，則r(a)= . 20.當(dāng) 時(shí)，矩陣a= 可逆.三、計(jì)算題： 1、設(shè)矩陣a= ，b=，求. 2、已知ax=b，其中a= ，b=（b=），求x. 3、已知ax=b，其中a= ，b=，求x. 4、設(shè)矩陣a= ，b= ,求解矩陣方程xa=b. 5、設(shè)矩陣a=

7、，計(jì)算.6、設(shè)矩陣a= ，計(jì)算.7、設(shè)矩陣a= ，i是3階單位矩陣，求.8、設(shè)矩陣a= ，b= ，求.9、設(shè)矩陣a= ，b= ，i是3階單位矩陣，求.10、設(shè)矩陣a= ，i= ，求.11、設(shè)齊次線性方程組，問(wèn)取何值時(shí)有非零解，并求一般解.12、討論為何值時(shí)，齊次線性方程組有非零解，并求一般解.13、求齊次線性方程組的一般解.14、求齊次線性方程組的一般解.15、討論當(dāng)為何值時(shí)，線性方程組無(wú)解，有唯一解，有無(wú)窮多解.16、求線性方程組的一般解.17、求線性方程組的一般解.18、當(dāng)為何值時(shí)，線性方程組有解，在有解的情況下求方程的一般解.19、當(dāng)為何值時(shí)，線性方程組有解，在有解的情況下求方程的一般解

8、.參考答案一、 單項(xiàng)選擇題：1.d 2.c 3.d 4.c 5.c 6.a 7.c 8.b 9.c 10.b 11.c 12.b 13.d 14.d 15.c 16.a 17.b 18.d 19.a 20.c 21.b 二、填空題：1.2 2.1 3.0 4.a、b為同階矩陣 5. 6.ab=ba7. 8.1 9.3 10.n 11. 12.r(a)=n13. (或 2 ) 14.n-r 15.-1 16.有非零解 17.318.-5 19.n 20. -3三、計(jì)算題： 1.解： , a-ii= ，所以 , =.2.解：ab= ，所以 （ ab= ，所以 )3.解法一：ai= 即 , 所以 =

9、 解法二：ab= ，所以4.解：ai= 即 ， = 5.解： , ，所以 6.解： ， ，所以 7.解：i-a= ，i-ai= ,所以= 8解： = ， ，所以= 9解：前面同第7題 = 10解： , 所以 11解：因?yàn)橄禂?shù)矩陣 a= 所以當(dāng)=4時(shí)，方程組有非零解，且一般解為：（其中為自由未知量）（或期末指導(dǎo)p.75三（13）12解：因?yàn)橄禂?shù)矩陣 a= 所以當(dāng)=4時(shí)，方程組有非零解，且一般解為： （其中為自由未知量）13解：因?yàn)橄禂?shù)矩陣 a= 所以方程組的一般解為：（其中是自由未知量）14解：因?yàn)橄禂?shù)矩陣a= 所以方程組的一般解為：（其中是自由未知量）15解：因?yàn)樵鰪V矩陣= 所以當(dāng)時(shí)，方程組無(wú)

10、解；當(dāng)時(shí)，方程組有唯一解；當(dāng)時(shí)，方程組有無(wú)窮多解.16.解：因?yàn)樵鰪V矩陣= ，故方程組的一般解為：（其中是自由未知量）17解：將方程組的增廣矩陣化為階梯矩陣= 由此得方程組的一般解（其中是自由未知量）18解：將方程組的增廣矩陣化為階梯矩陣= ，由此可知當(dāng)=3時(shí)，方程組有解，其一般解為（其中是自由未知量）19解：將方程組的增廣矩陣化為階梯矩陣= 由此可知當(dāng)=5時(shí)，方程組有解，其一般解為（其中是自由未知量） if we dont do that it will go on and go on. we have to stop it; we need the courage to do it.his

11、 comments came hours after fifa vice-president jeffrey webb - also in london for the fas celebrations - said he wanted to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says the matter has been exaggerated by the ivorian and the british media.blatter

12、, 77, said: it has been decided by the fifa congress that it is a nonsense for racism to be dealt with with fines. you can always find money from somebody to pay them.it is a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team

13、. it is all nonsense.we can do something better to fight racism and discrimination.this is one of the villains we have today in our game. but it is only with harsh sanctions that racism and discrimination can be washed out of football.the (lack of) air up there watch mcayman islands-based webb, the

14、head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt an

15、d i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the

16、 referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska.baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an imp

17、ortant role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weat

18、her lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of tur

19、bulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. still, hell be t

20、raveling fast, so despite the distance, it will not be like diving into the deep end of a pool. it will be like he is diving into the shallow end.skydiver preps for the big jumpwhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to earth. but this will not be enough to stop him completely.if